S-duality of the Leigh-Strassler Deformation via Matrix Models

Abstract

We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We perform non-trivial tests of the matrix model results against semiclassical field theory analysis. We also show that there are interesting points in parameter space where condensates can diverge and vacua disappear. Based on the matrix model results, we propose an exact elliptic superpotential to describe the theory compactified on a circle of finite radius.

33 pages, 2 figures, uses JHEP.cls; minus sign typo corrected and 1 reference added, submitted to JHEP

References in corpus (4)

• A Perturbative Window into Non-Perturbative Physics
• On Geometry and Matrix Models
• Quantum moduli spaces from matrix models
• World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials

Cited by in corpus (62)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Lax Pair for Strings in Lunin-Maldacena Background
• Green-Schwarz Strings in TsT-transformed backgrounds
• Exact Superpotentials for Theories with Flavors via a Matrix Integral
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• Exact superpotentials in N=1 theories with flavor and their matrix model formulation
• Konishi anomaly and N=1 effective superpotentials from matrix models
• Emergent geometry from q-deformations of N=4 super Yang-Mills
• S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Proof of all-order finiteness for planar beta-deformed Yang-Mills
• Baryons, Boundaries and Matrix Models
• Perturbative Derivation of Exact Superpotential for Meson Fields from Matrix Theories with One Flavour
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• Seiberg Duality in Matrix Model
• On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
• A New Deconstruction of Little String Theory
• Adding flavor to Dijkgraaf-Vafa
• Deformed PP-waves from the Lunin-Maldacena Background
• Seiberg Duality in Matrix Models II
• Loop equations, matrix models, and N=1 supersymmetric gauge theories
• Super Yang-Mills With Flavors From Large N_f Matrix Models
• Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with (Bi-)fundamental matters
• $\mathcal{N}=1$ Theories and a Geometric Master Field
• Precision Test of AdS/CFT in Lunin-Maldacena Background
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• Exact Mesonic Vacua From Matrix Models
• On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
• $\beta$-deformations, potentials and KK modes
• Note on Matrix Model with Massless Flavors
• Weak coupling large-N transitions at finite baryon density
• New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• Instanton test of non-supersymmetric deformations of the AdS_5 x S^5
• Generalized Yukawa couplings and Matrix Models
• The Anatomy of Gauge/String Duality in Lunin-Maldacena Background
• Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model
• The Coulomb branch of the Leigh-Strassler deformation and matrix models
• Pure Spinor Strings in TsT Deformed Background
• Instanton Calculations in the beta-deformed AdS/CFT Correspondence
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Master Space and Hilbert Series for N=1 Field Theories
• Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra
• Derivation of the linearity principle of Intriligator-Leigh-Seiberg
• Non-Critical Superstrings from Four-Dimensional Gauge Theory
• String theory dual of the beta-deformed gauge theory
• N=1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler
• Chiral primaries in the Leigh-Strassler deformed N=4 SYM -- a perturbative study
• Another Leigh-Strassler deformation through the Matrix model
• Matrix models for topological strings: exact results in the planar limit
• AdS/CFT Duality for Non-Anticommutative Supersymmetric Gauge Theory
• Solving matrix models using holomorphy
• Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
• Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models
• New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations
• $T^3$ deformations and $\beta$-deformed geometries
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• Marginal Deformations of N=4 SYM and Open vs. Closed String Parameters
• Matrix Model and beta-deformed N=4 SYM
• Dynamical SUSY Breaking and the Beta-Deformation